If x is equal to , where the given expressions extend to an infinite number of roots, then what is the value of x?a)-3b)-4c)3d)4e)12Correct answer is option 'D'. Can you explain this answer?

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GMAT Exam > GMAT Questions > If x is equal to , where the given expression...

If x is equal to

, where the given expressions extend to an infinite number of roots, then what is the value of x?

a)
-3
b)
-4
c)
3
d)
4
e)
12

Correct answer is option 'D'. Can you explain this answer?

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Verified Answer

If x is equal to , where the given expressions extend to an infinite n...

Given

to an infinite terms
- As the value of x is equal to the square root of something, x ≥ 0

To Find:

The value of x

Approach

to an infinite terms.

Since the expression under the root extends infinitely, the expression under the root will be equal to x itself.
So, 0………….(1)
By solving this equation and applying the constraint that x ≥0, we will find the value of x

Working Out

b. Squaring both sides, we have

As we know that x≥ 0, x = 4

Answer: D

Alternate solution

Once we have deduced that x will be positive the options -3 and -4 are eliminated
We know √9 is 3. So the value of √(12+ ……) will be more than 3. Now we are left with 4 and 12 in the options

Now √(12 + …..) cannot give us 12..
So the answer has be 4.

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